Insulation Gradient Math
I’d like to validate that I properly understand what I’m seeing with my bandboard insulation.
I live in zone 4a (St. Louis, MO) in a 90s era tract home. It’s been as cold as -5 recently. My bandboard is insulated with R-7.5 (1.5″ XPS) with 1 part spray foam around the edges then R-23 mineral wool on top of that. My house is 70-72 degrees in the basement with a RH of around 35%.
It’s my understanding that based on this setup, the surface of the foam should be around 14 degrees using the following equation:
Temp of foam = Inside Temp – ((Mineral wool R value/Assembly R value) * inside vs outside temp differential)
Temp of foam = 72 – ((23/30.5) * 77)
Temp of foam = 13.9 degrees
When I remove the mineral wool, the foam is actually around 45 degrees. Is this a theoretical vs reality difference or is my math significantly off? I realize the bandboard itself and sheathing add a point or two of r-value that I omitted for simplicity.
The mineral wool has accumulated some moisture and the XPS is damp on the surface. Not a huge amount but not a tiny amount either. Assume this is normal and expected for -5 degrees and will dry harmlessly to the inside once the weather warms?
If my math is correct and the XPS is expected to be 14 degrees and the dew point is around 40 degrees, moisture would be expected.
Can someone tell me if I’m thinking about all this correctly and if my system is appropriate and working as should be expected?
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Replies
How tight does the mineral wool fit?
See if you can get a thermometer that you can tape against the foam without a remote read out and leave it there for a long period of time while the mineral wool is in place.
It's a friction fit. Not loose yet not overly compressed.
I have a thermal camera and don't see major thermal leakage around the edges. There is some, but I don't think that's avoidable. It's possible the thermal camera which I'm using to measure surface temp isn't accurate.
Intuitively, I would expect the surface layer on foam insulation to warm up very quickly once you remove the mineral wool insulation (because it is a good insulator - there is less conduction to the rest of the foam which is cool and so that surface layer should normalize to room temperature very quickly. It's a super interesting experiment. Please post more results if you get a chance to try more experiments.
While this is not really helpful, you are ignoring a whole bunch of assembly R value stuff. The wood itself, the air layers.
And then time.
If your inside and out side temperatures had been the same for a really, really long time then the math may or may not work, but you cannot use the current temperature when that temperature may vary any large amount.
I think it should also be noted that things like R value are numbers that were created to compare things against other things, but not really against reality. We insulate a house and say it should use this much energy and then oversize the heat plant by 100 percent and say, 'hey that all worked, right?'
As insulation values go up, the heat flow drops, but the variables do not. At R30 you theoretically have 3 percent of the heatflow compared to R1 if calculate correctly, but all the inaccuracies stay the same
All I am saying is that to calculate good guess at fuel use, fine, but if a John Huston looking guy wants to make a bet with you about the temp in the middle of your wall that is a hard pass
[old Hitchcock reference there]